Question

Find zw and z/w, leave your answers in polar form.

z=6(cos 170° + i sin 170°) w=10(cos 200° + i sin 200°)
What is the product?
__ [ cos __ ° + sin __°]
(Simplify your answers. Type any angle measures in degrees. Use angle measures great)
What is the quotient?
__ [ cos __ ° + sin __°]

Answer 1

To find the product zw, we multiply the magnitudes and add the angles in polar form:
zw = 6(cos 170° + i sin 170°) * 10(cos 200° + i sin 200°)
zw = 60(cos 170° + i sin 170°)(cos 200° + i sin 200°)
zw = 60(cos 370° + i sin 370°)
zw = 60(cos 10° + i sin 10°)
The product is 60(cos 10° + i sin 10°).

To find the quotient z/w, we divide the magnitudes and subtract the angles in polar form:
z/w = 6(cos 170° + i sin 170°) / 10(cos 200° + i sin 200°)
z/w = (3/5)(cos 170° + i sin 170°)(cos(-200°) + i sin(-200°))
z/w = (3/5)(cos(-30°) + i sin(-30°))
z/w = (3/5)(cos 330° + i sin 330°)
The quotient is (3/5)(cos 330° + i sin 330°).